The brake/clutch unit of the well-known drive mechanism of the general type described above has a separate brake disk and clutch disk, which can be brought into frictional engaement, independently of one another, with the brake support and clutch support, respectively. The clutch and brake disks are either rigid in embodiment and displaceable on the driven shaft by means of a gear, or else axially resilient in embodiment and firmly connected with the driven shaft in the axial direction. Providing two such disks is expensive in terms of money as well as of manufacturing and construction effort and requires increased space. Since drive mechanisms of this kind are actuated extremely frequently--up to 30,000 operations comprising clutch engagement and braking occur in the course of one 8-hour shift--it is particularly important to minimize the noises associated with these actuations.